You can take a direct train to Malmö from Copenhagen Airport. From here it’s 20 minutes to Malmö Centralstation. You can get to Copenhagen Airport by both train and metro. Find train tickets here.
Please note that border authorities carry out ID inspection at Copenhagen Airport for travelers going to or from Malmö (or elsewhere in Sweden).
Tickets from the capital area to Southern Sweden are available for purchase at DSB Sales & Service within the capital area, 7-eleven stations or ticket machines.
Protip: Consider getting off at Triangelns Station which is one stop before Malmö Centralstation and boasts a quite spectacular arrival hall (pictured above). Above ground, you'll find the Triangeln shopping mall.
Take The Øresunds Bridge. From central Copenhagen to central Malmö this is ride takes about 45 - 60 minutes depending on the traffic. A one-way toll fee is about DKK 360. See the exact prices here.
In Ingerslevsgade, right off Copenhagen Central Station, you’ll find buses like Flixbus taking you back and forth.